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Related Concept Videos

Hückel's Rule Diagram of π MOs: Frost Circle01:08

Hückel's Rule Diagram of π MOs: Frost Circle

The Frost circle or the inscribed polygon method is a graphical method for determining the relative energies of π molecular orbitals (MOs) for planar, fully conjugated, and monocyclic compounds. This method was first described by A. A. Frost and Boris Musulin in 1953.
A Frost circle is constructed by drawing a polygon whose number of edges is equal to the number of carbons of the given cyclic system, with one of the vertices pointing down. Then, a circle is drawn enclosing the polygon so that...
Fermi Level01:18

Fermi Level

The Fermi-Dirac function is represented by an S-shaped curve indicating the probability of an energy state being occupied by an electron at a given temperature. The Fermi level is the energy level at which there is a fifty percent chance of finding an electron, and it is positioned between the lower-energy valence band and the higher-energy conduction band.
At absolute zero temperature, electrons fill all energy states up to the Fermi level, leaving upper states empty. As the temperature rises,...
Fermi Level Dynamics01:12

Fermi Level Dynamics

The vacuum level denotes the energy threshold required for an electron to escape from a material surface. It is usually positioned above the conduction band of a semiconductor and acts as a benchmark for comparing electron energies within various materials.
Electron affinity in semiconductors refers to the energy gap between the minimum of its conduction band and the vacuum level and it is a critical parameter in determining how easily a semiconductor can accept additional electrons.
The work...
[3,3] Sigmatropic Rearrangement of 1,5-Dienes: Cope Rearrangement01:21

[3,3] Sigmatropic Rearrangement of 1,5-Dienes: Cope Rearrangement

The Cope rearrangement is classified as a [3,3] sigmatropic shift in 1,5-dienes, leading to a more stable, isomeric 1,5-diene. The reaction involves a concerted movement of six electrons, four from two π bonds and two from a σ bond, via an energetically favorable chair-like transition state.
Potential Due to a Polarized Object01:29

Potential Due to a Polarized Object

A neutral atom consists of a positively charged nucleus surrounded by a negatively charged electron cloud. When placed in an external electric field, the external electric force pulls the electrons and nucleus apart, opposite to the intrinsic attraction between the nucleus and the electrons. The opposing forces balance each other with a slight shift between the center of masses of the nucleus and the electron cloud, resulting in a polarized atom. On the other hand, a few molecules, like water,...
¹H NMR: Long-Range Coupling01:27

¹H NMR: Long-Range Coupling

The coupling interactions of nuclei across four or more bonds are usually weak, with J values less than 1 Hz. While these are usually not observed in spectra, the presence of multiple bonds along the coupling pathway can result in observable long-range coupling.
In alkenes, spin information is communicated via σ–π overlap, as seen in allylic (four-bond) and homoallylic (five-bond) couplings. These coupling interactions are stronger when the σ bond is parallel to the alkene π orbitals.

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Related Experiment Video

Updated: May 7, 2026

Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving
11:21

Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving

Published on: March 30, 2017

A smooth polaron-molecule crossover in a Fermi system.

D M Edwards1

  • 1Department of Mathematics, Imperial College London, London SW7 2BZ, UK.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|October 1, 2013
PubMed
Summary

A single down-spin particle interacting with cold atoms shows a smooth crossover from polaron to molecule behavior as interaction strength increases. This challenges claims of a sharp transition in Fermi sea interactions.

Area of Science:

  • Atomic, Molecular, and Optical Physics
  • Condensed Matter Physics

Background:

  • Investigates the interaction between a single down-spin particle and a Fermi sea of up-spin particles, a key problem in cold atom physics.
  • Considers the Hubbard model for atoms in optical lattices and a parallel gas model.

Purpose of the Study:

  • To analyze the crossover behavior from polaron to molecule states as attractive interaction strength increases.
  • To clarify the nature of the transition between these two behaviors.

Main Methods:

  • Utilizes the Hubbard model and a gas model framework.
  • Examines the effects of varying attractive short-range interaction strengths.

Main Results:

  • Demonstrates a smooth crossover from polaron behavior (weak Fermi sea perturbation) to molecule behavior (bound state).

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Experimental Methods for Spin- and Angle-Resolved Photoemission Spectroscopy Combined with Polarization-Variable Laser
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Experimental Methods for Spin- and Angle-Resolved Photoemission Spectroscopy Combined with Polarization-Variable Laser

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A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
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A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

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Last Updated: May 7, 2026

Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving
11:21

Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving

Published on: March 30, 2017

Experimental Methods for Spin- and Angle-Resolved Photoemission Spectroscopy Combined with Polarization-Variable Laser
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Experimental Methods for Spin- and Angle-Resolved Photoemission Spectroscopy Combined with Polarization-Variable Laser

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A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

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  • Provides evidence that this crossover is continuous, not a sharp transition.

    • Conclusions:

    • The transition from polaron to molecule states in this system is a smooth crossover.
    • Contradicts previous claims of a sharp, discontinuous transition in the literature.